Can Hidden Variables Explain Correlation?∗

Correlations arise naturally in non-cooperative games, e.g., in the equivalence between undominated and optimal strategies in games with more than two players. But the non-cooperative assumption is that players do not coordinate their strategy choices, so where do these correlations come from? In coin tossing, correlated assessments are usually understood as reflecting the observer’s ignorance of a hidden variable—viz., the coin’s parameter or bias. We take a similar view of correlation in games. The hidden variables are the players’ characteristics that aren’t already described in the matrix or tree—viz., their types (beliefs about the game, beliefs about other players’ beliefs, etc.). A player may then consider other players’ strategies to be correlated, if he considers their types to be correlated. We analyze this hidden-variable view of game-theoretic correlation.